Answer
$10y^{3n}-6y^{2n}+5$.
Work Step by Step
The given expression is
$=(y^{3n}-7y^{2n}+3)-(-3y^{3n}-2y^{2n}-1)+(6y^{3n}-y^{2n}+1)$
Clear the parentheses.
$=y^{3n}-7y^{2n}+3+3y^{3n}+2y^{2n}+1+6y^{3n}-y^{2n}+1$
Add like terms.
$=10y^{3n}-6y^{2n}+5$.